Generalized Skewed Linnik Distribution and its Application in Time Series

Tarami, Bahram; Shirvani, Amin; Sajjadnia, Zahra

doi:10.22034/jirss.2025.2052626.1100

Generalized Skewed Linnik Distribution and its Application in Time Series

Document Type : Original Article

Authors

Bahram Tarami ¹

Amin Shirvani ²

Zahra Sajjadnia ³

¹ Department of Statistics, Science college, Shiraz University, Shiraz, Iran.

² Department of water engineering, Faculty of Agriculture, Shiraz university, Shiraz, Iran

³ Departments of Statistics, Shiraz University, Shiraz, Iran.

10.22034/jirss.2025.2052626.1100

Abstract

Heavy-tailed distributions have recently gained prominence in science, economics, and industry as robust alternatives to the Gaussian distribution, particularly for modeling data with extreme variability or outliers. Several studies in the literature have introduced and examined the Pakes generalized Linnik distribution and its related distributions due to their flexibility in capturing heavy-tailed behavior. However, most existing works focus exclusively on the special case of symmetric random variables—a significant limitation, given that real-world data often exhibit skewness. To address this gap, this paper proposes a new class of generalized skewed Linnik distributions, extending previous symmetric models to accommodate asymmetric data structures. We investigate their theoretical properties, including moments, tail behavior, and stability under linear transformations. Furthermore, we develop an autoregressive (AR) model based on this framework, enabling time-series analysis with skewed, heavytailed innovations. Additionally, we introduce a novel class of geometric skewed Linnik distributions, which arise as the limit of random sums and exhibit unique dependence structures. The practical utility of these models is demonstrated through theoretical derivations and potential applications in finance, risk assessment, and signal processing. Our results broaden the scope of Linnik-based models, offering more accurate tools for skewed, heavy-tailed data analysis.

Keywords

Skewed Linnink Distribution

Characteristic Function

Geometric Distribution

Autoregressive Process

Subjects

Applied Probability

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